各類梁的彎矩剪力計算匯總表

1、表1簡單載荷下根本梁的剪力圖與彎矩圖剪力Fs圖彎矩M圖an1 M e3備 L石Iil卜MeFsl(+q4 *“U 二心l注：外伸梁 =懸臂梁+端部作用集中力偶的簡支梁2.單跨梁的內(nèi)力及變形表(表2-6表 2-10)(1)簡支梁的反力、剪力、彎矩、撓度表2-6序次圖類圖工程反力朝力荷賽2彎短荷羲彎施算力荷裁Wini口 一口.nr一汽.2M2 =5H,出澆度反力剪力VA-RAi Vq + as).撓崖反力= K打力時Ijf I 48 E/Ra =牛 F t 口 H零期七uh統(tǒng)度W= 74KJ(3 7)剪力精載彎矩剪力a反力剪力彎審撓度反力剪力描度/?A Rr VAxfiAi vB= - r6Ma*

2、_ 19中W-3841V*-Ra; V&= -RbMx J /qf54 z - 384 EZ萍次圖類荷戴藥矩剪力荷載x4fn反力Ra= Rr= 剪力Rq Vh= -R3圖 示工程算式z撓度MaV 盤J f3-2八q反力剪力爐A一貫群VB= -當(dāng)工=U -當(dāng)時,FK!IUIIIIJi彎相f1 1I41 一/ J,撓度X闔LT-等田針時1HUI 1IJ11 HILy反力前力ir & . T/一一口1JtJ1/一/B一 汽修彎矩當(dāng)工二鼻+ T M=三1一時, 嚴(yán).4口 +筆用2引LXif饒度3盤12-號用x 工 r , *產(chǎn)J8段1 ukiiin1mp反方Rb吟niuniii8Li L 12!剪力V

3、=Ra；爐h=Rb1 L ：彎矩饒度Ma, =等 g 3pw = -* 384 FHilln卜小-應(yīng)渾 7 V8 仆1有短荷蒞等運翦力荷載穹痣境力序次圖類荷羲對短剪力示工程反力3 / 八=一34矩M掘底反力/?A =尺日=哂二曲金 241式中士 X = d +空3答,&=誓卡0卷L1荷較剪力彎柜呼速購力IIK!,unn撓宣計算式山%用Va=Ra; Vb= -J?bMa, - qba *=等-避-紀(jì)2懸臂梁的反力、剪力、彎矩和撓度表2-7序次圖類工程彎矩朝力荷穹期剪力荷戴rTrnrnTrrnTnunwiiiiiMiini一 rfTrfrnnTDTTOHT反力剪力彎矩?fù)隙确戳袅澙頁隙萺*fMr

4、=-F/ M111al=Mr=-FWrb=f_13EIMj - F (x - fl); Mm=Mej= - Ffr“u磬3-十序次圖類 示工程計 算 式l . nFt 1,_t i 自反力Rb= nF1,L q j,白.(f 1:才4卷r t剪力狀島工-f?B3彎矩鷺矩Ma -剪力梯度3M+ 4 四 + % 乜廠24曲兒m4荷載J反力R qlLJI 1ilbN1 1剪力VB= -Rbr才年矩加彎矩Mx=M-今明力CW撓度砒.5荷載A_ql!f! 1反力Re= a,T1氏1剪力%=-RbiZL學(xué)矩rnTnrnTI彎矩Mh .產(chǎn)一臂 2-fl)的力wnmni饒度2-=3=嘉介爺6荷載反力fi3-聃

5、/liU IL 口, * EJr1 由 Tl剪力vb=-Rb彎矩彎矩qb*M* - V算力7撓度5H 痣(4-,)序次用類圖 工程計 算 式7荷戴4,k_ 111川反力翦力VB- -Rn彎短雪矩Mb= _ Q品劉力wtmi攜度twA=2f Wb2l - 4tJ+ acl(3) 一端簡支另一端固定梁的反力、剪力、彎矩和撓度表2-8序次圖類圖 示工程計算式I荷載1 f 的反力%=磊臺 5技F剪力爐*=H解 * -B藥矩r,lu等矩Mb 4Fi Mb= _ 7T JZIOHllUIlllL 一一一一 tilllHU提度當(dāng)壬二 0,4471時,1rB = k 口09蒐害2荷教F反力丹3馱3-*11f

6、ri * . _ A二剪為VA= J?A VB= -kB尊矩rfTtl彎矩當(dāng)工a 時,剪力rmn1燒度CB身：1/于11. 一 上 *iitiimiiiiuiWi - r T lA 13 1-r - JJ - 3ro x + r t _r 一 Q J3荷羲反力A-f27亍7的工口 + -“信:剪力“火川 V6 -J?61/ J ;寸iF穹矩彎矩= Mc= Ra R.魯 - +llT一夕剪力vA=fiAi vB= -仁 一T*4Tf等矩0穹矩當(dāng)工=見時河0=票- x + qur* iuT ii! J.BC訕4Ra(3Njc-) - qa Q + IZWj:) 匕工+ 6aj2 - 4jJ當(dāng)工=a

7、 時*5 l/we【4&R 耳(3/一廣)-3qa (4/6 + a )qi.rrnfftt1k反力Ra=E +)I 2第8-岑 +專)匚IIf.b/上b二.,t射力VA= J?A； VB= - Hr6彎矩6雪姐當(dāng)工=q +拳時,乂皿二田/ fl +劄1uuiljlLLU剪力iPhTh撓度AC：TltE Ra .一工 一時!)UJC1BC段：Wj-14WA?3尸工-工,)-4g% + g (x a )當(dāng)工=a時*叫 近7 口R人 *-a*) 一被】Utlllllll 上彎羯ff當(dāng)M =叫+不時.時7;R*撓度ACS：wK- 24ff -4/?a 3Z! j - x 2L26k + if tCD

8、段：他.- 2% 4段 3產(chǎn)工一,一曲1助、譏工+ A j - iti*limuiiju剪力荷藪圄 示工程計 算 式4iqII 11 ,11 反力R駕1涉-4產(chǎn)+潟hRq我產(chǎn)M-Ra1剪力VA=1?A；y日一4兩端固定梁的反力、剪力、彎矩和撓度 表2-9剪力撓度當(dāng)然二晶時,V3EIf口十占序次國類圖 示工程計尊 式al .Il . jfjB反力Ka=R產(chǎn)/F荷載與_氣剪力 =R* Ve= - Rr1管矩蹲矩第力蹺度Wriu - 192E1 Jr-54a_反力3陰1號1 5部書荷戰(zhàn)L 1 一 1剪力3 Ra： Vb- -Rb2穹矩/4M彎矩 2F代產(chǎn) ml *7序次圖類ffi 示工程計 算 式3

9、荷載grrnrrn以反力R = R e 更A.Hjmmiminniiiiiiipr11l剪力R舀：廿日=一Kuf-1-, A / Lf彎矩d零短M二四 14LUllLL“力*IU4J撓度城 “2-3囪EI4荷載gqxljuihl iiunniLp反力jR % =宜目=1剪力v=Rq v= -rbtkA萼矩Mi考彎矩WILU史力口撓度5荷立q反力Rs- Co* + Wh(2-JZ_T剪力Va=VB= -fiB彎矩M _.jdTl彎電M4=-置6-8*+3/)* *于Xjaw當(dāng) r=上時 Mx = /+Ma牙2qUlllLL剪力撓度AC段t便/=由(-J?昌3,3MAJt*+手)BC 段：剪, =

10、 7 *- 3M、* 寧(u* = 4(a.+6*j*7#3r學(xué)走剪力JITIninr11撓度wc=普1 + 十當(dāng)工=心+0.5f 時,-0.0642riUD荷裁CI反力R * = R日=F匕箸/*1T剪力竄川二 一慶小爐H=氏日等矩1K彎矩Ma二 Mb- - FaL,力撓度叫=叫?=留S工力當(dāng)工=& + 0,51 時+ u- - 57oJqj序次JWt網(wǎng)類圖 示工程計 1K 式3荷裁g反力R4二號Il帚什C -JT甲*卜剪力Vae= - gtn 匕w = Klw： 丫廣.Rb1彎矩彎矩i,2假設(shè)I叫當(dāng)工=/(-11* Mz=宗司的力擄度吸=疆(7 + 4*3)4荷盤a反力RA=/?B=1+

11、2-J-) =- (l + 2fl)iiii.ii i1匚 ft D剪力丫收=零* VAe = y?h v = *yg/t 孽的=我W T寸 T彎矩穹重乂外一-上卿 Mw二職173)iHiiirmr剪力撓度J-器524%)5荷羲,孕反力T卜+土1:尤產(chǎn)號1 f -1 *剪力*3=一科】y爐二-b=以電力彎矩?fù)隙萂 n JU . = 宣.1 31A八一,密(,用當(dāng)上二口 + 0,423/時qa112序次工程國類反力剪力饒度反力物力7彎短irTTnTTrr狎力燒直反力mm7圖 示VA= - Ra; VB= RI tMa= Mb- t 2 Uc - WD剪力if 算 式式2+川8L7當(dāng)工=口+.同時

12、-黨Ra=與Zr型Rl 21VA= -f?A VB=/?n皿 , L hF誕*當(dāng)工=j .不時.Mg= 藥方3+十甩,uiiiiniiiiiiiiiH8那么力V*aS = 如: V fthi h=-Kb彎矩彎矩Mk與Mb=-i -2出其力提度L意(T*6$)9荷載%,M反力“空剪力心一 一 平 VAS= Y 產(chǎn) Rk彎布一 /rTTEyJII彎矩m* -軍 i4努力4Jlunjuinin程度叫嗡(1+荷教3.等截面連續(xù)梁的內(nèi)力及變形表1等跨連續(xù)梁的彎矩、剪力及撓度系數(shù)表表 2-11表2-141二跨等跨梁的內(nèi)力和撓度系數(shù)表2-11序次荷載圖路內(nèi)最大彎矩支座彎期剪 力|腭度中點撓度Mlm2MrVk

13、* %VC |叫皿21q0.0700.070-0.125仇375-0.6250.625-0,3750.5210.S21NIIiinii j lja fa j (Mi)(而2JllfjujJ ,T0.0961-0.0630.437-0.S63 0.11630.0630.912-0.3913- F 產(chǎn)4日Ctii0.1560.156-0.18S0 J12-0,6Ft80.68b1一 0,3120.9110.9114.F_ _. 4aKABC0.203-0.0940.406-0.5940.094 0.0941.497-CI.SS65金 色i -+ 0,2220-222一D,3m3.即-1.3331.

14、333-0.6671.4661.4666F 分 含*10.278L-0.167.&33-1.1670,16704672.5OSL1.042注：1.在均布荷載作用下：=表中系數(shù)*ql2; 丫 =表中系數(shù)X ql； w表中系數(shù)ql4 J o100EI2.在集中荷載作用下： =表中系數(shù)*Fl; 丫=表中系數(shù)X F; w 表中系數(shù)Fl3 o100EI例1二跨等跨梁l = 5m,均布荷載q=11.76kN/m,每跨各有一集中荷載 F=29.4kN,求中間支座的最大彎矩和剪力.解|支=(- 0.125X 11.76X 52) + ( 0.188X 29.4X5)=( 36.75) + (-27.64) =

15、 - 64.39kN - mVb左=(- 0.625X 11.76X 5) + ( 0.688X 29.4)=( 36.75) + ( 20.23) = - 56.98kN例2解三跨等跨梁l = 6m,均布荷載q=11.76kN/m,求邊跨最大跨中彎矩.M1 =0.080X11.76X 62=33.87kN m.2三跨等跨梁的內(nèi)力和撓度系數(shù)表 2-12荷載圖博內(nèi)最大 彎距文座彎短剪 力蹲度中點捷度%MbI Me算的1VD加1 J, 必-叫3,0800,025-0.100-0.100口,400-0.6000.500-0.5000,&00-0,4000.6770.0520.677inittHiri

16、iiiiriiEittfitiB次由 x荷1教圖算內(nèi)最大| 萼麗1支座耳矩W 力跨度中點撓度MtMiMbMcvAVBS爐品%噎VDWi2皿2I_0.101-0.05(1-0.D3C0.450-0.55(1(100.550 |-0.45.0.990-0.625O.WOJL JHHAc 33nil1IH一口 M5-o.oso-0.05Q-0.050- 0.050 0,500-0.5000+0500.050-0.313Q.677-0.313;2 B40.073隊054-0.117-0.0330.383-0.6170,583-0,417O.OJ30.0330.5730.365-0.208li 11|

17、It 金235I/5f*j1&8c 臺0.094-0.0670.0170.433-0.5670.0830.083-0,017-0.0170.8S5-0.3130.1046r 今涵$ 4_LrJ8mB0,175).100-0415fl-0,1500.350-0,65.0.51)0-0,500 仇65.-0.3501.1460.2081.1467r .JF? %).213-0.075-0.0750.425-0.575 0fl0.575-0.425lr6lS-0.9371,6158f 2,?8a.i75-0.075-0.075-0.075-0,0750.500-0,5000.0750.075-0.4

18、691.146-0.4699合dACD3,162J, 1370.175-0,收0325-0.6750.625-0.3750,0500*0500.9900.677-0.312*次荷載圖畤內(nèi)最大雪矩支座彎地剪 力算度中點燒度MMiMhMcvAVstr% 喂vD訕lW上必10“J 120C-o.ioq0.0250.400-D.6000.1250.U5-0.025-0,0231.458-0.夠 90,156A8CD11產(chǎn)1產(chǎn)力1尸_4i g ?8h24dp.O670.267-0,2610.733-1.2671,000-l.OOO i,267-0.733L8830.2161,期12有 口h腳-0.133

19、rO.lH.也-1.134001.B4-IL8662716-1謠72.7討13ABCDL2M-0.133-0.133-0.133-0.1331.0001.00Q0.ROJ33-0.8331秘37用14fl T 4 E;e x 自0,2升DJ7C-0.311l,-0,0B93爐觥 (V -0.62S0一出 6387-0.6550-0.6737-0.650-(L7IS7-0.7450-0,77378網(wǎng)-0,3W7-0.R7500.9766-1.煙k (3Q.62500.67610x72920.7836Q.g駁30. (1958必953】L01H)1.U6941,12831.18751-33681.

20、4K75心-Q.3750 -0.4239 -0.47080.5164 -0.5607-ft MM2 0.6469 -0.6K90 -0.7306 -0-7717 -0.8125 -0.9132 -1.0125加冊 (Mz) 0.Q9S?0.0970 0.0982 0.0993 0.1003Q. 1.門 0.1021 0.102 O.lOl? 0.1044 0.1050 0.1065 0.1Q7SVA (VJ J0.43750.44050.44320.44570,4479(M5190.4537U.45M0.45690.45S3仇 46150.4M3Mir0.0957仇 11420,134?0.1

21、558IL 17880.20320.22910.25MO.28SO031550.34720.45270.5272!匕-0.4375-Q.478D-0.5182-(L55R2 0.5979 -0.6375-0.6769-0.7162-0.7554-0.7944-O.JI333-0.93B-1.026 fs注：1. =表中系數(shù)x ql2i； 丫=表中系數(shù)X qli； 2. Mmax、Vmax表示它為相應(yīng)跨內(nèi)的最大內(nèi)力.祀MbY AH1 vA蕈桔產(chǎn)防Mb (MM眈uMahVAf JMbu?Ma)0.4-0.08310.0B69口,4169 0.58310.2000-0.M620,5962(h4頒08

22、900.必 1.0,01500.5-0,08W0.088000.】out%0.5804-0.5800g5M 0.0947-0,5470.45020.0918&.42S60.02230.6-0,08000,0882-0.00口 OCI0,.30000.0952-0.59520.46030.09431.4J420.0W80.7-0.0HL90.UH740.021160.4181-U.58L90,3500-0.09TO-0.5970.482$0.09640,43900.04030.80.0S57-0.00590.4141-U.5K59,1.4000-0.1021-0.60210.51160,(198

23、20.4432Q.O5U90.9-0.09180.0B330.0093D,40S2-fl.59180,4500-0.1083-0.6Q830.54fl.09980 . 44&S0.06231.0-IhlOOO0.00000.02500.41MK)0,60000.5000-0.11670.61670.5833040130.45(X10.075ftJJ-0.11 IX)6,07615 3 鞏)0-0.61000.5500-0. J2670626?0.62330.10250,45280.0SS51.2-0.121KU.07150.05820.3782-fl.621gQ.MKK)-0J3H5-0.65

24、H50.66510. HB70,45540J0291J-0.13551 0.06640.07580.36450.63550.65fK)(h 15220.65220.70820.10J70.45761Q,l21.4-0.15100,06090.09400.3490-0.51.0,7000-D,lfi760.66760.75250J0570.45970.13441,5一0 J戰(zhàn)30.05500.11300.3317-0.6683Q.75OO一.JR4H-0.6K4R0.7976030650.461504514-k40.04890.13270.31-0.6S730.8000-0.2037-0.703

25、70 84340 10730,46S20.16941,70.20820.04260.15310.29180.70820.8500-0.2244-0,72440.88970+10SO&.464S0,1883L8 1-0.25080.0320.1742(L26920.73080. woo-0.2468-0.74680.9366i). 10870,46620.20801.9-0.2555D.03000,19610.244S0.75520.9500-0,2710-0,77100.9S460.10930.46750.22S62.0-0.2M30.02390.21B80.218-0.7813I.UOIK)

26、-0.29690.79691,03120.10990.46 跳0.25002.25-035400.01060.27 岫0J4620.R5381.1250-0.3691(L86911.15110 JillQ.47140.30742.5-ft.43750,00140.3437-0.0625-0.9375L25O0-Or452l0,95211.2722 !QJ12Z0.4737ft.37012三不等跨梁內(nèi)力系數(shù)表 2-16注：1. =表中系數(shù)* q|2i - 丫=表中系數(shù)X qll； 2 . M max、 V max為荷載在最不利布置時的最大內(nèi)力.4.雙向板在均布荷載作用下的內(nèi)力及變形系數(shù)表(表 2

27、-17表 2-22)符號說明如下:剛度K12(12)式中 E一一彈性模量;h板厚;v泊松比;、max分別為板中央點的撓度和最大撓度;Mx為平行于lx方向板中央點的彎矩;MyMx0為平行于ly方向板中央點的彎矩;-固定邊中點沿lx方向的彎矩；My0固定邊中點沿ly方向的彎矩.正負(fù)號的規(guī)定:彎矩一一使板的受荷面受壓者為正；撓度 變位方向與荷載方向相同者為正.四邊簡支表2-17I.彎矩-表中系數(shù)篤嫉式中,取八和與中之較小者出W以My0*5.0.010130.0945(L0174QJ)O6fl30.05610.03340,550.009400.08920.021U0.H50.005470.05060.

28、0J4B0.60口的8Q0.082O.必20.00460.0456O.QW0.650.0750().02710.950.004490.04100,0364(L7O0.0()727.皎30.02 輛1.000,004060.03680.0368O.7J0.M6630.06200.0317IHIIIIBIIITI三邊簡支,一邊固定表2-18mH 三 IE澆度二表中系數(shù)K考速三表中系教工布工式中1取人和仆中之較小者,J與訕 tnU1sMM?MiMyM?0,50U.005040.05830.0060-0.1212I 0.950.0U3240.03240.0280-0.0820.55O.OCM92僅 0

29、563O.UOfilrf) .11870.900,003680,0翼 80,0322-D.O9260.600.004720.05390.0104 0.11580.E50.004170.03290370-0.09700.65k004480.05130.0116211240.00fl.004730.03260.U42W-0JU140,700.00422O.(M85Q.014S-Q.107C.750.005360.03190.U485-0.10560.75.一 003網(wǎng).川570.A168-0,104810,70Q006050.0308a.0553一./.96.屈0.003760.04280,018

30、7-0J0070.65 10.006800.02910.0627-0.1133Ik 850.003520.04000.0204*0.09650.8D0.DD7620.02480,0707-031660.900,003290.03720.0219-0.0923D.550.M8M0.02390.0792-0, J1930.950.003060,03450.0232-O.0K800,500.0093S0.02050.0880-0,1215LOOl.Ofl0.00285U.O3I90.0243兩邊簡支,兩邊固定表2-19“4WM工M?1 I J Kw,以My0.500.002610.04160.001

31、7-0.0M30.95Q.002230,02960.0189- 0.07460.550,002590,0410Q.uimOH4n0.9D0.00260U.U3060.0224-0,07970.64)0.002550.0402O.(HM2-0334045O.CbO3O30.03140.02660.08500.650.002500.03920.0057-0,08260.800.003540.03190.0316-U.O5MJ40.700.002430.03790,0072-0.0B140,750.004L3(LQ321(3.03740.750.002360,03660.00fi8-0.07990.

32、700.004820.03180.04410J0130.SD0.002280.03510.0103-0.078255IL00S60(hl3O80.0J13-(klD6fe0.850.00220,.335O.QUSOh 07630.600.006470.D29Z0.0604-0.11140.900.001110.03190.0133-0.0743*50,1X)7430.02670,0698-0.11560.950.002010,0302.ni46-D .D72110.500,00844O.fi2340.0798-0.11911.00LOO0,001920.02850.01580,0698一邊簡支

33、,三邊固定表2-20rL二口二-Vr蘭出蜀一展l.W?rrif f(撓度=寰中聚數(shù)乂W K彎矩=表中系數(shù)Kq產(chǎn) 式中工取和乙中之較小者1w遙山噴W,P Id.mi*M.MrM;闈！0.S00.002580, D4O80. (M2H一0一0836-0.05690.550.002550 03980.0042-0.08270+05700.600.002490JJJS40.0059-0.05710.650.CW2400.03680.0076-0.07960.05720.700.002290,03500.0093-0.0774-0.05720.750,002190.1)3310.0109-0.0750-

34、0,05720聞0.002060.03100.0124-0.0722-0.05 的0.B50.001960-02890.013B-0.0693-0,05670.900.001840,02680,0159-0.0661-0.05630力5(1.001720.0247D.U0-0.C631-O,QS591.M1.000.001600,02270.01680.0600-0.05500-95O.OOU20.0229.M0.0629905的0.90(1.002060,02280,0223-0,0656-.加53D.A50.002330.02250.0255-0.0683 0.0711O.KO0.002620 02190.0290-0.0707-007720.7S0